# General Physics (PHY 2130)

Size: px
Start display at page:

## Transcription

1 General Physics (PHY 130) Lecture 0 Rotational dynamics equilibrium nd Newton s Law for rotational motion rolling Exam II review

2 Lightning Review Last lecture: 1. Momentum: momentum conservation collisions in one and two dimensions Review Problem: An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. She does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. A highway curve has a radius of 85 m. At what angle should the road be banked so that a car traveling at 6.8 m/s has no tendency to skid sideways on the road? (Hint: No tendency to skid means the frictional force is zero.)

3 Review Problem An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. She does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. A highway curve has a radius of 85 m. At what angle should the road be banked so that a car traveling at 6.8 m/s has no tendency to skid sideways on the road? (Hint: No tendency to skid means the frictional force is zero.) y θ N Take the car s motion to be into the page. Draw FBD and apply Newton s Second Law: v ( 1) Fx = N sinθ = mar = m r F = N cosθ w = ( ) 0 y w θ x Divide (3) by (4): Rewrite (1) and (): ( 3) N sinθ = m v r ( 4) N cosθ = mg ( 6.8 m/s) ( 9.8 m/s )( 85 m) v tanθ = = gr θ = 5.1 = 0.089

4 Last time: what if two or more different forces act on lever arm?

5 Net Torque The net torque is the sum of all the torques produced by all the forces Remember to account for the direction of the tendency for rotation Counterclockwise torques are positive Clockwise torques are negative

6 Example 1: Determine the net torque: N 4 m m Given: weights: w 1 = 500 N w = 800 N lever arms: d 1 =4 m d = m 500 N 1. Draw all applicable forces 800 N Find: Στ =?. Consider CCW rotation to be positive τ = (500 N)(4 m) + ( )(800 N)( m) =+ 000 N m 1600 N m =+ 400 N m Rotation would be CCW

7 Where would the 500 N person have to be relative to fulcrum for zero torque?

8 Example : N y d m m Given: weights: w 1 = 500 N w = 800 N lever arms: d 1 =4 m Στ = 0 Find: d =? 500 N 800 N 1. Draw all applicable forces and moment arms τ τ RHS LHS = (800 N)( m) = (500 N)( d m) 800 [ N m] d [ N m] = 0 d = 3. m According to our understanding of torque there would be no rotation and no motion! What does it say about acceleration and force? Thus, according to nd Newton s law ΣF=0 and a=0! F i = ( 500 N) + N' + ( 800 N) = 0 N' = 1300 N

9 Torque and Equilibrium First Condition of Equilibrium The net external force must be zero ΣF = 0 ΣF x = 0 and ΣF y = 0 This is a necessary, but not sufficient, condition to ensure that an object is in complete mechanical equilibrium This is a statement of translational equilibrium Second Condition of Equilibrium The net external torque must be zero Στ = 0 This is a statement of rotational equilibrium

10 Axis of Rotation So far we have chosen obvious axis of rotation If the object is in equilibrium, it does not matter where you put the axis of rotation for calculating the net torque The location of the axis of rotation is completely arbitrary Often the nature of the problem will suggest a convenient location for the axis When solving a problem, you must specify an axis of rotation Once you have chosen an axis, you must maintain that choice consistently throughout the problem

11 Center of Gravity (center of mass) The force of gravity acting on an object must be considered In finding the torque produced by the force of gravity, all of the weight of the object can be considered to be concentrated at one point

12 Calculating the Center of Gravity 1. The object is divided up into a large number of very small particles of weight (mg). Each particle will have a set of coordinates indicating its location (x,y) 3. The torque produced by each particle about the axis of rotation is equal to its weight times its lever arm 4. We wish to locate the point of application of the single force, whose magnitude is equal to the weight of the object, and whose effect on the rotation is the same as all the individual particles. This point is called the center of gravity of the object

13 Coordinates of the Center of Gravity The coordinates of the center of gravity can be found from the sum of the torques acting on the individual particles being set equal to the torque produced by the weight of the object x cg = Σm x i Σm i i and y cg = Σm y i Σm i i The center of gravity of a homogenous, symmetric body must lie on the axis of symmetry. Often, the center of gravity of such an object is the geometric center of the object.

14 Example: Find center of gravity of the following system: Given: masses: m 1 = 5.00 kg m =.00 kg m 3 = 4.00 kg lever arms: d 1 =0.500 m d =1.00 m Find: Center of gravity x cg = m x i m i i m1x1 + mx + m3x = m + m + m kg( 0.500m) +.00 kg(0 m) kg(1.00 m) = 11.0 kg = 0.136m 3 3

15 Experimentally Determining the Center of Gravity The wrench is hung freely from two different pivots The intersection of the lines indicates the center of gravity A rigid object can be balanced by a single force equal in magnitude to its weight as long as the force is acting upward through the object s center of gravity

16 Equilibrium, once again A zero net torque does not mean the absence of rotational motion An object that rotates at uniform angular velocity can be under the influence of a zero net torque This is analogous to the translational situation where a zero net force does not mean the object is not in motion

17 More on Free Body Diagrams Isolate the object to be analyzed Draw the free body diagram for that object Include all the external forces acting on the object

18 Example Suppose that you placed a 10 m ladder (which weights 100 N) against the wall at the angle of 30. What are the forces acting on it and when would it be in equilibrium?

19 Example: Given: weights: w 1 = 100 N length: l=10 m angle: α=30 Στ = 0 Find: f =? n=? P=? 1. Draw all applicable forces. Choose axis of rotation at bottom corner (τ of f and n are 0!) Torques: Forces: L τ = mg cos30 PLsin = 100 N P 1 P = 86.6 N α = 0 F F mg x y = f P = 0 f = 86.6 N = n mg = 0 n = 100 N f 86.6 N Note: f = µ s n, so µ s = = = n 100 N

20 So far: net torque was zero. What if it is not?

21 Torque and Angular Acceleration When a rigid object is subject to a net torque ( 0), it undergoes an angular acceleration The angular acceleration is directly proportional to the net torque The relationship is analogous to F = ma Newton s Second Law

22 Torque and Angular Acceleration F F r, ( ma ) tangential a t t t = = ma = rα, so t multiply by t F t r = r r acceleration : mr α torque τ dependent upon object and axis of rotation. Called moment of inertia I. Units: kg m I Σm r i i τ = Iα The angular acceleration is inversely proportional to the analogy of the mass in a rotating system

23 Newton s Second Law for a Rotating Object The angular acceleration is directly proportional to the net torque The angular acceleration is inversely proportional to the moment of inertia of the object Στ = Iα There is a major difference between moment of inertia and mass: the moment of inertia depends on the quantity of matter and its distribution in the rigid object. The moment of inertia also depends upon the location of the axis of rotation

24 Example: Consider a flywheel (cylinder pulley) of mass M=5 kg and radius R=0. m and weight of 9.8 N hanging from rope wrapped around flywheel. What are forces acting on flywheel and weight? Find acceleration of the weight. mg

25 Example: N I = 1 MR = 0.10 kg m T Given: Mg T masses: M = 5 kg weight: w = 9.8 N radius: R=0. m mg 1. Draw all applicable forces Find: Forces=? a t T = = αr or or I R a t Forces: Torques: F = mg T = ma need T! Tangential acceleration at the edge of flywheel (a=a t ): a t TR = I 0.10 kg m = ( 0. m) a t = (.5kg ) a t a = F = mg T = ma mg mg τ = T R = I α (.5kg ) ( m +.5kg ) a t 9.8 N = 3.5kg T R α = I = ma =.8m s

26 Note on problem solving: The same basic techniques that were used in linear motion can be applied to rotational motion. Analogies: F becomes τ, m becomes I and a becomes α becomes ω and x becomes θ Techniques for conservation of energy are the same as for linear systems, as long as you include the rotational kinetic energy Problems involving angular momentum are essentially the same technique as those with linear momentum The moment of inertia may change, leading to a change in angular momentum, v

27 Review before Exam Useful tips: 1. Do and understand all the homework problems.. Review and understand all the problems done in class. 3. Review and understand all the problems done in the textbook (chapters 4-7). 4. Come to office hours if you have questions!!!

28 Exam Review

29 Review problem The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure 1. If the spring is compressed a distance of 0.10 m and the gun fired vertically as shown, the gun can launch a 0.0-g projectile from rest to a maximum height of 0.0 m above the starting point of the projectile. Neglecting all resistive forces, determine (a) the spring constant and (b) the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure 1.

30

### Chapter 8. Rotational Equilibrium and Rotational Dynamics

Chapter 8 Rotational Equilibrium and Rotational Dynamics 1 Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related 2 Torque The door is free to rotate

### Chapter 8. Rotational Equilibrium and Rotational Dynamics

Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about

### Application of Forces. Chapter Eight. Torque. Force vs. Torque. Torque, cont. Direction of Torque 4/7/2015

Raymond A. Serway Chris Vuille Chapter Eight Rotational Equilibrium and Rotational Dynamics Application of Forces The point of application of a force is important This was ignored in treating objects as

### We define angular displacement, θ, and angular velocity, ω. What's a radian?

We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise

### = o + t = ot + ½ t 2 = o + 2

Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the

### PHYSICS 149: Lecture 21

PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30

### Uniform Circular Motion

Uniform Circular Motion Motion in a circle at constant angular speed. ω: angular velocity (rad/s) Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle,

### Torque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.

Warm up A remote-controlled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics

### Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and

Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about

### Announcements Oct 27, 2009

Announcements Oct 7, 009 1. HW 14 due tonight. Reminder: some of your HW answers will need to be written in scientific notation. Do this with e notation, not with x signs. a. 6.57E33 correct format b.

### Chapter 8. Centripetal Force and The Law of Gravity

Chapter 8 Centripetal Force and The Law of Gravity Centripetal Acceleration An object traveling in a circle, even though it moves with a constant speed, will have an acceleration The centripetal acceleration

### Moment of Inertia Race

Review Two points, A and B, are on a disk that rotates with a uniform speed about an axis. Point A is closer to the axis than point B. Which of the following is NOT true? 1. Point B has the greater tangential

### PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1

PHYSICS 220 Lecture 15 Angular Momentum Textbook Sections 9.3 9.6 Lecture 15 Purdue University, Physics 220 1 Last Lecture Overview Torque = Force that causes rotation τ = F r sin θ Work done by torque

### Chapter 8. Rotational Equilibrium and Rotational Dynamics

Chapter 8 Rotational Equilibrium and Rotational Dynamics Wrench Demo Torque Torque, τ, is the tendency of a force to rotate an object about some axis τ = Fd F is the force d is the lever arm (or moment

### Review for 3 rd Midterm

Review for 3 rd Midterm Midterm is on 4/19 at 7:30pm in the same rooms as before You are allowed one double sided sheet of paper with any handwritten notes you like. The moment-of-inertia about the center-of-mass

### Physics 101 Lecture 11 Torque

Physics 101 Lecture 11 Torque Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Force vs. Torque q Forces cause accelerations q What cause angular accelerations? q A door is free to rotate about an axis

### Chapter 8 continued. Rotational Dynamics

Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = s = rφ = Frφ Fr = τ (torque) = τφ r φ s F to s θ = 0 DEFINITION

### Physics 111. Lecture 22 (Walker: ) Torque Rotational Dynamics Static Equilibrium Oct. 28, 2009

Physics 111 Lecture 22 (Walker: 11.1-3) Torque Rotational Dynamics Static Equilibrium Oct. 28, 2009 Lecture 22 1/26 Torque (τ) We define a quantity called torque which is a measure of twisting effort.

### Static Equilibrium; Torque

Static Equilibrium; Torque The Conditions for Equilibrium An object with forces acting on it, but that is not moving, is said to be in equilibrium. The first condition for equilibrium is that the net force

### Chapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics

Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I

### PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)

PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when

### Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs.

Agenda Today: Homework quiz, moment of inertia and torque Thursday: Statics problems revisited, rolling motion Reading: Start Chapter 8 in the reading Have to cancel office hours today: will have extra

### Chapter 8 Lecture Notes

Chapter 8 Lecture Notes Physics 2414 - Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ

### Chapter 9. Rotational Dynamics

Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

### CHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque

7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity

### Rotational Dynamics continued

Chapter 9 Rotational Dynamics continued 9.1 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :

### PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011

PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this

### 31 ROTATIONAL KINEMATICS

31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have

### Slide 1 / 37. Rotational Motion

Slide 1 / 37 Rotational Motion Slide 2 / 37 Angular Quantities An angle θ can be given by: where r is the radius and l is the arc length. This gives θ in radians. There are 360 in a circle or 2π radians.

### Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics

Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av

### Rotational Dynamics. Slide 2 / 34. Slide 1 / 34. Slide 4 / 34. Slide 3 / 34. Slide 6 / 34. Slide 5 / 34. Moment of Inertia. Parallel Axis Theorem

Slide 1 / 34 Rotational ynamics l Slide 2 / 34 Moment of Inertia To determine the moment of inertia we divide the object into tiny masses of m i a distance r i from the center. is the sum of all the tiny

### Translational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work

Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational

### Chapter 8 continued. Rotational Dynamics

Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF

### Chapter 10. Rotation of a Rigid Object about a Fixed Axis

Chapter 10 Rotation of a Rigid Object about a Fixed Axis Angular Position Axis of rotation is the center of the disc Choose a fixed reference line. Point P is at a fixed distance r from the origin. A small

### Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a

### Physics 1A Lecture 10B

Physics 1A Lecture 10B "Sometimes the world puts a spin on life. When our equilibrium returns to us, we understand more because we've seen the whole picture. --Davis Barton Cross Products Another way to

### FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing 2.

### Rotational Dynamics continued

Chapter 9 Rotational Dynamics continued 9.4 Newton s Second Law for Rotational Motion About a Fixed Axis ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS I = ( mr 2

### Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 2

Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 1 3 problems from exam 2 6 problems 13.1 14.6 (including 14.5) 8 problems 1.1---9.6 Go through the

### Chapter 8 continued. Rotational Dynamics

Chapter 8 continued Rotational Dynamics 8.6 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :

### Physics 101 Lecture 12 Equilibrium and Angular Momentum

Physics 101 Lecture 1 Equilibrium and Angular Momentum Ali ÖVGÜN EMU Physics Department www.aovgun.com Static Equilibrium q Equilibrium and static equilibrium q Static equilibrium conditions n Net external

### Welcome back to Physics 211

Welcome back to Physics 211 Today s agenda: Torque Rotational Dynamics Current assignments Prelecture Thursday, Nov 20th at 10:30am HW#13 due this Friday at 5 pm. Clicker.1 What is the center of mass of

### Plane Motion of Rigid Bodies: Forces and Accelerations

Plane Motion of Rigid Bodies: Forces and Accelerations Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,

### Rotational Kinematics and Dynamics. UCVTS AIT Physics

Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,

### Rotational Kinetic Energy

Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body

### Exam 3 Practice Solutions

Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

### Static Equilibrium, Gravitation, Periodic Motion

This test covers static equilibrium, universal gravitation, and simple harmonic motion, with some problems requiring a knowledge of basic calculus. Part I. Multiple Choice 1. 60 A B 10 kg A mass of 10

### Torque. Introduction. Torque. PHY torque - J. Hedberg

Torque PHY 207 - torque - J. Hedberg - 2017 1. Introduction 2. Torque 1. Lever arm changes 3. Net Torques 4. Moment of Rotational Inertia 1. Moment of Inertia for Arbitrary Shapes 2. Parallel Axis Theorem

### Chapter 10. Rotation

Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGraw-PHY 45 Chap_10Ha-Rotation-Revised

### PHYS 185 Final Exam December 4, 2012

PHYS 185 Final Exam December 4, 2012 Name: Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Please make an effort

### Chapter 9- Static Equilibrium

Chapter 9- Static Equilibrium Changes in Office-hours The following changes will take place until the end of the semester Office-hours: - Monday, 12:00-13:00h - Wednesday, 14:00-15:00h - Friday, 13:00-14:00h

### Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular

Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only

### α = p = m v L = I ω Review: Torque Physics 201, Lecture 21 Review: Rotational Dynamics a = Στ = I α

Physics 1, Lecture 1 Today s Topics q Static Equilibrium of Rigid Objects(Ch. 1.1-3) Review: Rotational and Translational Motion Conditions for Translational and Rotational Equilibrium Demos and Exercises

### Chapter 8 - Rotational Dynamics and Equilibrium REVIEW

Pagpalain ka! (Good luck, in Filipino) Date Chapter 8 - Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body

### Physics 111. Lecture 23 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, Kinetic Energy of Rolling Object

Physics 111 Lecture 3 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, 009 Lecture 3 1/4 Kinetic Energy of Rolling Object Total kinetic energy of a rolling object is the sum of

### Chapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.

Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium

### Welcome back to Physics 211

Welcome back to Physics 211 Today s agenda: Moment of Inertia Angular momentum 13-2 1 Current assignments Prelecture due Tuesday after Thanksgiving HW#13 due next Wednesday, 11/24 Turn in written assignment

### Chapter 9-10 Test Review

Chapter 9-10 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular

### Physics 201, Lecture 18

q q Physics 01, Lecture 18 Rotational Dynamics Torque Exercises and Applications Rolling Motion Today s Topics Review Angular Velocity And Angular Acceleration q Angular Velocity (ω) describes how fast

### Lecture 14. Rotational dynamics Torque. Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

Lecture 14 Rotational dynamics Torque Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes, 87 1 BC EXAM Tuesday March 6, 018 8:15 PM 9:45 PM Today s Topics:

### Webreview Torque and Rotation Practice Test

Please do not write on test. ID A Webreview - 8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30-m-radius automobile

### AP Pd 3 Rotational Dynamics.notebook. May 08, 2014

1 Rotational Dynamics Why do objects spin? Objects can travel in different ways: Translation all points on the body travel in parallel paths Rotation all points on the body move around a fixed point An

### Physics A - PHY 2048C

Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment

### Chapter 12 Static Equilibrium

Chapter Static Equilibrium. Analysis Model: Rigid Body in Equilibrium. More on the Center of Gravity. Examples of Rigid Objects in Static Equilibrium CHAPTER : STATIC EQUILIBRIUM AND ELASTICITY.) The Conditions

### Chapter 10: Dynamics of Rotational Motion

Chapter 10: Dynamics of Rotational Motion What causes an angular acceleration? The effectiveness of a force at causing a rotation is called torque. QuickCheck 12.5 The four forces shown have the same strength.

### 1.1. Rotational Kinematics Description Of Motion Of A Rotating Body

PHY 19- PHYSICS III 1. Moment Of Inertia 1.1. Rotational Kinematics Description Of Motion Of A Rotating Body 1.1.1. Linear Kinematics Consider the case of linear kinematics; it concerns the description

### Physics 201, Lecture 21

Physics 201, Lecture 21 Today s Topics q Static Equilibrium of Rigid Objects(Ch. 12.1-3) Review: Rotational and Translational Motion Conditions for Translational and Rotational Equilibrium Demos and Exercises

### FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is

### Class XI Chapter 7- System of Particles and Rotational Motion Physics

Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie

### 2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity

2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity Energy 7 4 Kinematics Free fall Collisions 3 5 Dynamics

### Chapter 8: Rotational Motion

Lecture Outline Chapter 8: Rotational Motion This lecture will help you understand: Circular Motion Rotational Inertia Torque Center of Mass and Center of Gravity Centripetal Force Centrifugal Force Rotating

### Circular Motion Tangential Speed. Conceptual Physics 11 th Edition. Circular Motion Rotational Speed. Circular Motion

Conceptual Physics 11 th Edition Circular Motion Tangential Speed The distance traveled by a point on the rotating object divided by the time taken to travel that distance is called its tangential speed

### Rotational Motion and Torque

Rotational Motion and Torque Introduction to Angular Quantities Sections 8- to 8-2 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is

### Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1

Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 1. A 50-kg boy and a 40-kg girl sit on opposite ends of a 3-meter see-saw. How far from the girl should the fulcrum be placed in order for the

### 4) Vector = and vector = What is vector = +? A) B) C) D) E)

1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In

### Rotation. PHYS 101 Previous Exam Problems CHAPTER

PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that

### Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Strike (Day 10) Prelectures, checkpoints, lectures continue with no change. Take-home quizzes this week. See Elaine Schulte s email. HW

### Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)

Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position

### DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-5: ROTATIONAL DYNAMICS; TORQUE AND ROTATIONAL INERTIA LSN 8-6: SOLVING PROBLEMS IN ROTATIONAL DYNAMICS Questions From Reading Activity? Big Idea(s):

### Physics 4A Solutions to Chapter 10 Homework

Physics 4A Solutions to Chapter 0 Homework Chapter 0 Questions: 4, 6, 8 Exercises & Problems 6, 3, 6, 4, 45, 5, 5, 7, 8 Answers to Questions: Q 0-4 (a) positive (b) zero (c) negative (d) negative Q 0-6

### Mechanics II. Which of the following relations among the forces W, k, N, and F must be true?

Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which

### FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Monday, 14 December 2015, 6 PM to 9 PM, Field House Gym

FALL TERM EXAM, PHYS 111, INTRODUCTORY PHYSICS I Monday, 14 December 015, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing. There

### Torque/Rotational Energy Mock Exam. Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK.

AP Physics C Spring, 2017 Torque/Rotational Energy Mock Exam Name: Answer Key Mr. Leonard Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK. (22 pts ) 1. Two masses are attached

### Chapter 9. Rotational Dynamics

Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination

### Physics. Chapter 8 Rotational Motion

Physics Chapter 8 Rotational Motion Circular Motion Tangential Speed The linear speed of something moving along a circular path. Symbol is the usual v and units are m/s Rotational Speed Number of revolutions

### Chapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:

linear momentum: Chapter 8: Momentum, Impulse, & Collisions Newton s second law in terms of momentum: impulse: Under what SPECIFIC condition is linear momentum conserved? (The answer does not involve collisions.)

### Review questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.

Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the

### AP Physics 1 Rotational Motion Practice Test

AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able

### PH1104/PH114S MECHANICS

PH04/PH4S MECHANICS SEMESTER I EXAMINATION 06-07 SOLUTION MULTIPLE-CHOICE QUESTIONS. (B) For freely falling bodies, the equation v = gh holds. v is proportional to h, therefore v v = h h = h h =.. (B).5i

### CHAPTER 9 ROTATIONAL DYNAMICS

CHAPTER 9 ROTATIONAL DYNAMICS PROBLEMS. REASONING The drawing shows the forces acting on the person. It also shows the lever arms for a rotational axis perpendicular to the plane of the paper at the place

### Final Exam Spring 2014 May 05, 2014

95.141 Final Exam Spring 2014 May 05, 2014 Section number Section instructor Last/First name Last 3 Digits of Student ID Number: Answer all questions, beginning each new question in the space provided.

### Chapter 12. Static Equilibrium and Elasticity

Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial

### Chapter 9. Rotational Dynamics

Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

### PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from

### Torque. Physics 6A. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Physics 6A Torque is what causes angular acceleration (just like a force causes linear acceleration) Torque is what causes angular acceleration (just like a force causes linear acceleration) For a torque

### ω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2

PHY 302 K. Solutions for problem set #9. Textbook problem 7.10: For linear motion at constant acceleration a, average velocity during some time interval from t 1 to t 2 is the average of the velocities

### Chapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics

Chapter 12: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational 2 / / 1/ 2 m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv 2 /

### PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from